1. Field of the Invention
The present invention relates to a method for designing waveforms of RF pulses for use in an excitation sequence in magnetic resonance tomography.
2. Description of the Prior Art
Currently clinical magnetic resonance (MR) systems use a single RF transmitting channel for emitting radio-frequency pulses to excite nuclear spins in an examination subject. The use of a single RF transmit channel imposes limitations in several applications of MR imaging, such as high-field and whole body imaging.
The use of multiple, independent RF modulators and RF coils is the subject of current investigation, and holds promise for mitigating some of the limitations imposed by the use of single RF transmit channel, by providing additional degrees of freedom.
A significant concern associated with multi-channel transmission is a potentially higher specific absorption (SAR), due to the larger number of simultaneously transmitting channels.
When RF pulses are designed using a conventional matrix inversion by means of a singular value decomposition (SVD), this results in a higher RF peak and RMS power than is necessary to achieve excitation within specified designed constraints. Therefore, SAR and pulse power (peak and RMS) ca, in theory, be reduced without a comprise in excitation quality.
Some of the many negative consequences of high SAR are that the flip angle cannot be set to the desired value, which degrades the signal-to-noise ratio (SNR) and image contrast, the SAR online supervision switches off the RF power during the measurement, thereby delaying or stopping the scan, artificial limits are imposed on the number of achievable slices, and an increase in repetition time (TR) is required, which translates into longer scan times.
Furthermore, conventional RF design algorithms lead to higher artifact levels in images due to their poor numerical properties. For example, images may exhibit incomplete background suppression, poor spin cancellation, or suboptimal excitation of desired target regions.
Parallel RF excitation in the presence of 2-D and 3-D gradient trajectories offers a flexible means for spatially-tailoring excitation patterns for inner-volume excitation (J. Pauly, et al. A k-space analysis of small-tip angle excitation. J. Magn. Reson. Med., 81:43-56, 1989) and to address increased B1-inhomogeneity observed at high field strengths due to wavelength interference effects as described in V. A. Stenger et al. B1 Inhomogeneity Reduction with Transmit SENSE. 2nd International Workshop on Parallel Imaging, page 94, 2004. Zurich, Switzerland. Small tip angle three-dimensional tailored radiofrequency slab-select pulse for reduced B1 inhomogeneity at 3 T (J. Magn. Reson. Med., 53(2):479-484, 2005, and J. Ulloa and J. V. Hajnal. Exploring 3D RF shimming for slice selective imaging. ISMRM, page 21, 2005. Miami Beach, Fla., USA). These pulses are useful because they may be tailored to impose an arbitrary spatial pattern on the transverse magnetization's magnitude and phase, subject to the constraints on RF and gradient hardware. The implementation of a 3-channel parallel excitation system was first shown by Ullmann et al. in Experimental analysis of parallel excitation using dedicated coil setups and simultaneous RF transmission on multiple channels. J. Magn. Reson. Med., 54(4):994-1001, 2005. More recently, researchers designed an 8-channel parallel excitation system on a 3T human scanner, demonstrating fast slice-selective uniform excitation and high resolution 2-D spatial shape excitation
A parallel excitation system consists of a set of coil arrays capable of independent, simultaneous RF transmission. Assuming that the set of gradient waveforms is fixed (i.e., the k-space trajectory is pre-determined), the B1 maps of the coil arrays are known, and that a desired complex-valued target excitation pattern is chosen, it remains necessary to design a set of RF waveforms for the coil array to perform the specified spatially-tailored excitation. The primary limitation of such an excitation is the length of time needed for the pulse. A parallel excitation system circumvents this limitation by allowing one “accelerate” the k-space trajectory via undersampling, which leads to a reduction in RF pulse duration. An acceleration factor of R for a spiral trajectory means that the radial separation between spiral samples is increased by a factor of R relative to the unaccelerated Nyquist-sampled design. This acceleration is possible due to the extra degrees of freedom introduced by the system's multiple excitation coil arrays, analogous to acceleration in parallel reception.
Due to their complexity and nonlinearity, the equations relating the RF waveforms and target excitation are fast linearized using Grissom et al.'s formulation (W A. Grissom, et al. A new method for the design of RF pulses in Transmit SENSE. 2nd International Workshop on Parallel Imaging, page 95, 2004. Zurich, Switzerland), which is essentially the application of the ubiquitous small-tip angle approximation to parallel systems, as noted in the aforementioned article by Pauly et al. Other valid approaches to solving this system have been presented by Katscher et al., Transmit SENSE. J. Magn. Reson. Med., 49(1):144-150, 2003, who solve the system in k-space, and Zhu et al. Parallel excitation on an eight transmit channel MRI system. ISMRM, page 14, 2005. Miami Beach, Fla., USA, who formulate the problem in the spatial domain assuming an echo-planar k-space trajectory. All of these formulations greatly simplify the design process by reducing the design problem to solving a linear system equations. After linearizing the parallel RF equations, each of the three RF waveform design methods is used to design RF pulses. Each of the techniques is a different way of solving the system of equations and, because of finite-precision effects, yields a different set of RF waveforms. Each set of waveforms, in turn, leads to a unique excitation pattern and hence different excitation artifacts.
The conventionally employed algorithm used in MR technology makes use of an approximate pseudo-inverse generated by a singular value decomposition (SVD). This is popular for least-squares problems in many application areas and easy to justify analytically as discussed in G. H. Golub et al. Matrix Computations. Johns Hopkins University Press, 1983 and G. Strang. Introduction to linear Algebra. Wellesley-Cambridge Press, 1993. This will be referred to herein as the “SVD-based method”.